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This lesson is part of the following series:

Once you have learned how to find the Greatest Common Factor (GCF) of a set of numbers, you can simplify fractions by factoring the numerator and denominator until they are relatively prime. Numbers are relatively prime when they have no common factors, other than 1. To do this, you will need to find the GCF for the numerator and denomentator, and then divide them both by this factor. This will effectively simplify the fraction to its most simplified form.

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Pre Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/prealgebra. The full course covers whole numbers, integers, fractions and decimals, variables, expressions, equations and a variety of other pre algebra topics.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions. Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

About this Author

Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.

Recent Reviews

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A lot of times you can take a fraction and simplify it to an equivalent one, where in fact the numerator and the denominator have no common factors. We say they’re relatively prime. Let’s take a look at some examples, and see if we can simplify four-fifteenths. Can this be simplified at all? Is there any common factor that the numerator and denominator has? This is 2 times 2, and the denominator is 3 times 5. They have no factors in common. This is simplified; in its lowest terms. That’s it: four-fifteenths. That’s what we can say. No problem.

How about this example? Negative 18 over 30. I notice there is at least one common factor, because both of these numbers are even. This is 2 times something, and this is 2 times something. If you look a little bit closer we see that 3 is a factor of both of these, right? This is 3 times 6, and this is 3 times 10. I’ve got a common factor of 2 and a common factor of 3. Therefore, 6 should be a common factor of both the numerator and the denominator. Let’s see. Take a look at 18, I see that’s 6 times 3. Take a look at 30, I see that’s 6 times 5. So I can simplify this by dividing the numerator and the denominator by 6.

If you want to simplify this fraction, that’s fine. But if you divide the denominator by some value, in this case 6, to keep this fraction equivalent to the original one, we have to divide the numerator by the exact same amount. In this case, 6. What happens when we simplify this? Negative 18 divided by 6 is negative 3, divided by 30 divided by 6, that’s 5. Notice that 3 and 5 are relatively prime, they share no common factors greater than 1. So 1 is their greatest common factor; you can’t simplify it anymore. Negative three-fifths is the simplified equivalent fraction to negative 18 over 30. Look how we got rid of the common factor by dividing the numerator and denominator by that greatest common factor. What’s left over is the fraction written in simplest terms. Pretty cool.

Look for common factors and keep factoring things out. Keep dividing top and bottom by the same numbers, until you come down to two numbers that are relatively prime. Awesome.

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